Abstract:
Gruetl"\;'s method determi L1CS all Ihe roots of univariate polynomials both real and complex,
repeated ill1dnon-repeated simultaneollsly.ln lhi~ thesis, it I, ~aid that this ~la\Cmcnt is no!
universally [me, It is shown tilat the method is valid if the algebraic cq\lation~ ~alisfy the
condition~,
(i) equations with zero coellidcnt lll\l~l have at leasl one pair of equidistant llon-~cro
coeJTicient from the /,cro coefficient.
(ii) any transformed equation of a given ~quation with n01\-7£1'O coefficient may have zero
coefficients but these new cocffici~nt5 must satisfy (i).
(iii) all the coel1icicnts ofnlln-lincar equation must nol be unity.
GRAEFFE.BAS program 19] ha, been modified in these light and has been extended for nol
~()Ivabje equations.